As more and more businesses and individuals search for improved ways to protect important documents and valuables, a new industry is developing across the nation. In cities such as Atlanta, Dallas, New York, Beverly Hills, and Cincinnati, independent non-bank companies are now getting into the business of renting out safety-deposit boxes. Many have such attractive features as 365-day access, pickup and delivery service, and roomier boxes for large items.

The new safe-deposit services are tapping a market that banks apparently are unequipped to fill. Banks not only have limited hours, many of them also lack sufficient vault space for safe-deposit boxes -- particularly in the larger sizes. On Manhattan's Upper East Side, for example, the waiting list at banks for larger boxes -- those measuring, say, 3"X10"X24" and up -- can be several years, says Bruce Bodner, co-founder of a new service called First City Safe Deposit Co., which is opening in New York this month. While the most popular boxes are around the size of a bread box, some operators, such as Federal Safe Deposit Company of Beverly Hills, which opened in March, offer them in dimensions up to 5'X2 1/2'X5' for storing art and other bulky items.

Many of the non-bank safe-deposit companies are open around the clock, at least on weekends. This makes it possible, for example, for customers to pick up their best jewels on the way to the ball and return them on the way home. Some boxes can be rented on a one-day basis only. Annual rents vary according to size and market. For instance, a 10"X10"X24" box generally runs from $450 a year in Cincinnati to $550 in Beverly Hills. The largest sizes rent for $2,000 to $3,000 a year. On many popular sizes, prices are at least twice those at banks, but can often be offset by lower insurance rates for the depositor -- or a tax deduction if the use is investment-related.

Besides appealing to individuals, the private vault companies are also attracting business and professional clients, especially attorneys and investment advisers. Documents such as wills and securities certificates can be stored and retrieved with a minimum of planning. And Franklin D. Bryant, a partner at Federal Safe Deposit in Beverly Hills, notes that some companies that keep critical data like accounts receivable and inventory on computer tape are stashing back-up copies in their safe-deposit boxes as protection in case of fire or theft. Says Bryant: "A typical business client could be any company that uses a computer."